How do two waves travel through eachother, coming out unchanged?

My question initially came to me as I was thinking about standing waves, in that how do waves interfere, and then come out unchanged after this interference? For simplicities sake, imagine we have two wave pulses coming toward eachother on a string. Now lets say they are out of phase, so when they hit, there will be points when the string will be completely flat...i.e. complete destructive interference. My question is this...how do the waves progress past this point? Is it not the same as a wave suddenly appearing out of a string? All the particles are motionless at destructive interference point, so how do they "know" (I don't like using that term but its the only way I can think to put it) that they are going to form a wave afterward? If so, then where does the energy come from to do this, as in either case the energy is at a minimum as the particles are not moving, and then they suddenly are all moving, thus having energy that has magically appeared from somewhere??? I think there are similar implications for constructive interference too...

This all stemmed, as I said before, from standing waves, and how a wave can pass through a nodal point...again with this I'm somewhat stumped too.

The energy of a wave on a string is carried by the oscillation of atoms (or molecules) of the string. Even though, at some instant in time the displacement of all atoms is zero, the atoms are still moving, so the energy of the wave is still present.

The energy of a wave on a string is carried by the oscillation of atoms (or molecules) of the string. Even though, at some instant in time the displacement of all atoms is zero, the atoms are still moving, so the energy of the wave is still present.

OK thats a good point, and I'm embarrassed I didn't think of that, however I have some queries with it.

Firstly, wouldn't this oscillation of atoms just mean the string is warmer than before so to speak? To maintain the energy of the string, then the atoms themselves must gain more kinetic energy, thus greater kinetic energy means greater temperature. Now I think these oscillations would be random...they would be no way linked between molecules, so how then would one regenerate the wave? Then if this could happen, then wouldn't heating a string have the same effect, and shouldn't it form a wave (which I believe strings aren't renowned for doing).

Secondly, how do you explain this for EM radiation, for isn't it just energy (ignoring the fact are EM fields as I don't think this makes much difference)? Therefore there would be no molecules to oscillate and gain the energy when the destructive interference occurred, so does that not just imply the energy is just sitting there while the destructive intereference occurs? Then how a wave reforms out of that, I have no idea.

When I meant atoms oscillating I didn't mean in a thermal sense, rather as a means of dividing the string into infinitesimal sections.

The same principle applies for EM waves, the energy is stored in fields rather than the motion of objects. It is not just the absolute value of the EM fields that are important, but also the rate of change of these fields (as evidenced by the importance of the dE/dt and dB/dt terms in Maxwell's equations) that matters as well, just as velocity was important in addition to absolute displacement in the case of the string.

Hmmm I don't understand what you mean by the infinitesimal lengths. What other way is there for particles to store the energy of the wave while none are moving, other than their own movement, i.e. temperature?

Ah I don't have a clue about Maxwells equations so far, however its on my list of things to do. As a matter of fact I still don't even see how light can be a field, as in how is a ray of light, or a photon a three dimensional field? Is it a disturbance in such a field? No that wouldn't work, as then there'd need to be an EM field over the whole universe.

Sorry for the two questions, should probably stick to the first, otherwise we'll get off topic : )

1) Imagine a sting of an odd number of points. A sinusoidal wave starts at one end, and its perfect mirror starts at the other at precisily the same time and magnituted at the other. When the waves meet at the hypothetical midpoint they both exert exactly the same pressure, in exactly the opposite phase to each other and perfectly cancel out.

2) Imagine the same string with an even number of points. The waves meet only at a perfectly at a pointless place (pun intended). The waves, at the nearest "point" they can interecact do so unequally creating unequall pressures. As a result they "eat" each other at differing rates resulting in on a macro scale (one following the gross zero line) a halving in the power of both waves, and on a micro scale ( one following the relative zero line) a quartering of the power of the waves, but a doubling of the frequency. (The ripple of the passing of the waves through each other is carried on each departing waves surface) This is the very rough theoretical mechanism by which AM radio works as an example.

So firstly I assume then that you are assuming that all wave mediums are "even" so to speak, and that #1 doesn't actually occur in reality?? I think your explanation went somewhat over my head, but are you simply saying that in reality, when waves interfere destructively as before, its not perfect...i.e. a smaller wave actually travels along the string?? However would this wave not be easily observable, as with double the frequency and a quarter the power, the amplitude would still be sufficient to be observable would it not? If I'm way off track could you maybe refer a website? I don't have the knowledge of terms etc to find one myself...and I've looked a few times

And how this again applies to EM radiation...should it not have an infinite number of "points" so could be odd (or symmetrical about a point) so that number 2 could not occur?

kcodon. You are correct. #1 happens exceedingly rarely in the real world. Think in terms of radio and a signal that two antennae picked up even a few inches apart, the signals are not exactly the same strength, etc. so when they get whacked together they produce an interference pattern, not the same signal. It's how we do signal triangulation amongst other things.

Yes, it is observable, and sometimes a bad thing. That's why in radio a tank circuit of a capacitor and an inductor are placed in parallel in the system. Basically to "smooth" out the bumps and pay attention to the the big stuff, and throw away the little ripples. Or you could build the tank to throw away the big stuff and just pass the tiny ripples. Depends on what information you wish to capture and observe.

As for the mediums bit. The thought experiment said assume they were even. If even if you use #1, but the waves are identical, and opposite, but of different strength, say you were closer to emmiter A than emmiter B the waves would not anhillate each other completely. In that respect (the complete destruction of BOTH waves your observation is correct, it almost never happens).

Bottom line. Number Two almost ALWAYS occurs. Then we filter off whether we want the gross bits and ignore the ripple (AM) or ignore the gross bits and filter off the ripple (FM). A bit of a simplification, but it works. Turn on your car radio...lol.

Your explanation is great in terms of electronics, and EM radiation etc, but I was hoping for an explanation in terms of a string. So again I looked on Google, and to my embarrasment, i realised i had forgotten to put "energy" into my searches, along with other things. And after reading some of the stuff, I think I get it now...

For the string, all the energy of the wave is kinetic energy. Although at that instance of destructive interference the string is flat, the particles at the antinodal points must be moving faster etc, and thus have kinetic energy.

As for EM radiation, one can either think of it that there are certain points of no energy (nodes) however this gives consequential points of more energy (antinodes) i.e. double slit experiment. Or think of it that if one cancels completely the electric field of the waves, then the magnetic fields must have added thus energy conserved.

Anyways I think now I've sorted that one out, so thanks all, and hope the above helps,